Within such an approach, a time hierarchy of the physical
stages, through which the system passed during its evolution
toward equilibrium (starting from the kinetic stage via
intermediate steps till the hydrodynamic one and beyond
[1]}), appears quite naturally. The corresponding
time scales within that hierarchy can serve as a basis for
generalized hydrodynamics, in particular, in generalized
collective mode theory (GCM) [2]}, [3]}, where the set of
dynamical variables for description of long- and short-time
correlations usually consists of the densities of conserved
quantities and their time derivatives up to a certain order. Using
a physically reasonable assumption in the Markovian approximation
[4]} for the kinetic kernels of higher orders, one actually
comes to a simple mathematical problem, expressing collective
processes in the system in terms of the dynamic eigenmodes:
complex/real eigenvalues for propagating/relaxing processes and
corresponding eigenvectors which characterize contribution of
particular eigenmode to relevant correlations. A definite
advantage of the GCM is the fact that such a theory is a computer
adapted one: all the elements of the generalized dynamic matrix
could be expressed via the static correlation functions (SCF) and
corresponding relaxation times, which can be obtained by molecular
dynamic simulations [4]}, [6]}.
